This invention relates to the art of cursors for slide rules, particularly lineal slide rules.
The design of electrical circuits or power line networks for utilities frequently requires the resolution of complex networks of series and parallel impedances into resultant impedances. In some cases, one or more of the impedances in the circuit or power line network under consideration may be purely resistive, in which case the circuit analysis is significantly simplified. However, circuit impedances are commonly a complex mixture of resistance and reactance, a result of resistive, capacitive and inductive elements. In instances where the impedance of an element or network includes capacitive and/or inductive reactance portions, the impedance will include an imaginary component, and will be expressed in trigonometric vector form as R+JX, where R represents the real portion and JX the imaginary portion of the impedance. This trigonometric vector term R+JX may be converted into a corresponding phasor vector by squaring the portions of the trigonometric vector term, and then taking the square root of the sum of the squared portions. The phasor vector is expressed as Z/.theta., where Z corresponds to the quantity of the impedance, and .theta. corresponds to the angle of the phasor vector. These vector relationships are conventional and are illustrated in FIG. 1. FIG. 1 shows the relationship between the trigonometric vector form of an impedance of R+JX and the phasor vector form Z/.theta.. The phasor vector term is a single part resultant of the two-part trigonometric vector term R+JX.
The resolution of complex series and/or parallel impedances into a resultant impedance requires a significant number of laborious hand operations. This is particularly when the resultant of two parallel impedances is to be found. The resultant of two parallel impedances is found by the following formula: 1/Zp/.theta.p = 1/Z.sub.1 /.theta..sub.1 + 1/Z.sub.2 /.theta..sub.2. Typically, the solution of two parallel impedances can take more than thirty separate operations in order to obtain the correct values of Z.sub.p and .theta..sub.p, while a somewhat fewer number of operations are necessary to solve for the resultant of two series impedances. There are, of course, almost an infinite number of possible combinations of impedances, and hence, no tables are available for conveniently ascertaining the resultant of series or parallel impedances.
As a practical measure, the hand calculations in such instances are not made in their entirety but rather, an estimate is made as to the resultant values of Z or .theta.. Such a practice, although almost necessary as a practical measure, is undesirable, as it can lead to significant errors in the determination of resultant circuit impedance.
From the foregoing, it is a general object of the present invention to provide a slide rule cursor adapted for use with conventional slide rules to solve the problems in the art discussed above.
It is a further object of the present invention to provide such a slide rule cursor which can be used to determine the resultant Z and .theta. of parallel and/or series impedances in a relatively simple manner.
It is another object of the present invention to provide a slide rule cursor by which the resultant of series and/or parallel impedances may be obtained entirely by slide rule operations.
It is a still further object of the present invention to provide such a slide rule cursor which can also be used to solve conventional mathematical problems,
It is a further object of the present invention to provide such a slide rule cursor which is similar in size to conventional slide rule cursors.